Print BAM file downsampled to coverage at given loci

I'm trying to print a bam file downsampled to a certain coverage at given loci. What I've tried thus far is to use PrintReads with -dcov XXX, but as the documentation states, it will downsample to that coverage based on the beginning of the aligned read. Is there a way to get a bam file that has been downsampled to a (nearly) precise coverage at specified loci?

I am not using GATK to call variants or any other purpose, so I can't do it while calling variants.